If I understand your question correctly, it sounds like the vet did a exploratory surgery without your authorization. You signed an initial treatment plan for the costs of hospitalization. I cannot vouch for any other terminology contained within the estimate you signed, but generally, yes, I would expect the vet to at least call you at your emergency contact numbers to get your permission to do the surgery.
Now, there can be exceptions. Some treatment plans will include context that states in the event of an emergency, do you authorize the vet to do life-saving treatment. If you initialed that type of statement, that it gets very controvesial whether the consent is truly given.
In reality, I can't personally imagine doing a exploratory surgery without having called you first at every contact number you would have provided me.
I also can't comment whether a procedure was necessary or not necessary based on being life threatening.
It does sound a bit awkward if you were not contacted, at all, prior to surgery.
Hope that information helps.
I am not a lawyer, but just my general opinion on how I operate in my practice.